Several neurodegenerative diseases, such as Alzheimer's disease, cause atrophy of the cerebral cortex. Measurements of cerebral cortical thickness and volume can be used in the quantification and location of atrophy. While it is possible to measure the thickness of the cerebral cortex manually from magnetic resonance (MR) images, partial volume effects (PVE), orthogonality problems, large amounts of manual labour and operator bias makes it difficult to make measurements on large patient populations. Automatic quantification and localisation of atrophy is a highly desirable goal, as it allows studying early changes and track disease progression on large populations. A first step in achieving this goal is to develop robust and accurate methods for automatically measuring cortical thickness and volume.
The cortical thickness can be measured as the distance between the inner and outer boundaries of the cerebral cortex. Current research aims at automatically extracting these boundaries by means of rather complicated computer routines from digital data-sets of MR images. Typical MR images show the surrounding skull, inside which the brain, comprising the cerebrum, the cerebellum and the brain stem, is embedded in a cerebrospinal fluid (CSF). In the so-called T1-weighted (the T1 modality is described in “Principles of Medical Imaging” by K. Kirk Shung, Michael B. Smith and Benjamin Tsui, ISBN: 0-12-640970-6) MR images, CSF appears dark in the images in contrast to the white matter (WM) of the cerebrum. The outer layer of the cerebrum is the cerebral cortex, which in the T1-weighted images appears as grey matter (GM). The majority of known methods either extract the cortical boundaries directly from the image data, or they iteratively fit deformable surfaces to the boundaries from some initial configuration. The first approach typically segment CSF voxels, GM voxels, and the WM voxels in the volumetric MR image data based on the image intensities, and then extracts the boundary surfaces using an iso-surfacing algorithm like the marching cubes algorithm by William E. Lorensen and Harvey E. Cline, “Marching cubes: A high resolution 3D surface construction algorithm,” Computer Graphics, vol. 21, no. 4, pp. 163-169, 1987 U.S. Pat. No. 4,710,876 and U.S. Pat. No. 4,885,688. Voxel-based segmentation methods are often fast, reliable and well-suited for volumetric measurements. However, with the voxel-based methods, which most often rely on low-level image information, it is difficult to compensate for PVEs, and to obtain a sub-voxel accuracy.
Another approach, called the deformable surface approach, is typically a variation upon the active contour method due to Michael Kass, Andrew Witkin, and Demetri Terzopoulos, “Snakes: Active contour models,” International Journal of Computer Vision, 1988, where a curve, guided by an energy function, is fitted to the boundary of interest. The energy function consists of internal energies, which describe intrinsic properties of the curve and external energies which express external forces, such as the image gradient, which act upon the curve. Laurent D. Cohen and Isaac Cohen generalised the active contour framework to three dimensions, where a surface is fitted instead of a curve in “Finite-element methods for active contour models and balloons for 2D and 3D images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993.
The deformable surface approach makes it possible to compensate for PVEs to a higher degree than the voxel/iso-surface approach and in addition allows for obtaining sub-voxel accuracy, as surface deformation relies on both low-level as well as high-level information. The combination of high- and low-level information enables delineation of the boundary in areas where image edges are obscured or missing. Such areas are almost always present in MR images of the human cerebral cortex due to the convolved nature of the cortex and MR image related artifacts. Opposite banks of tight sulci may meet inside the sulcal folds and appear as connected in MR images due to undersampling and artifacts. The main difficulty in cortical segmentation lies in correctly penetrating such sulci and reaching their fundus, which is a very important aspect as the true cortical thickness could be over- or underestimated otherwise. David MacDonald, Noor Kabani, David Avis, and Alan C. Evans addressed this problem by deforming the outer and inner surface simultaneously under the influence of an intersurface distance constraint, which keeps the surfaces within some predefined distance, in “Automated 3-D extraction of inner and outer surfaces of cerebral cortex from MRI,” published in NeuroImage, vol. 12, pp. 340-356, 2000. The constraint drags the outer surface toward the fundus of sulci, although they might appear closed, and constraints prevent the surfaces from intersecting each other and themselves. However, there exist a bias between the chosen predefined distance and the measured cortical thickness leading to uncertainties in the final measurements.
A different approach to modeling the cortex without a distance constraint is taken by Anders M. Dale, Bruce Fischl, and Martin I. Sereno, “Cortical surface-based analysis i: Segmentation and surface reconstruction,” NeuroImage, vol. 9, pp. 179-194, 1999. In this approach, a surface, represented by a discrete mesh, is first fitted to the inner boundary of the cortex, and extended towards the outer boundary of the cortex in the direction of the surface normals. Such an approach places the surface at approximately the midpoints of tight sulci when no CSF is evident in between the sulcal banks, provided no self-intersections are allowed. The inner boundary follows the concavities and convexities of the outer boundary, but does in contrast to the outer boundary not appear as closed in tight sulci and is thus more easily segmented. Surface normals, approximated from a discrete mesh, may be inaccurate, as they can be perturbed by noise in the surface, and the surface normals may not always point in the correct direction of the second boundary. As the direction of the displacement of the deforming surface is only based on the surface normals, modelling of non-existing features may erroneously arise, when the surface is displaced over larger distances. A single mis-leading normal may for example cause modelling of a non-existent sulcus on the crown of a gyrus.
Chenyang Xu, Dzung L. Pham, Maryam E. Rettmann, Daphne N. Yu, and Jerry L. Prince, uses another approach in “Reconstruction of the human cerebral cortex from magnetic resonance images,” published in IEEE Transactions on Medical Imaging, vol. 18, no. 6, pp. 467-480, 1999. They introduced an interesting alternative with a “Generalised Gradient Vector Flow” (GGVF) force, which provides vectors pointing toward the nearest image edge. This force is then used for extending the inner surface towards the central layer of the cortex. Xu et al. noted that their approach could be tailored to segmenting the CSF/GM boundary instead of the central layer. However, their approach does not impose self-intersection constraints, which is necessary when segmenting the outer boundary. This method is not automatic but requires intervention and correction by an operator which makes this method time consuming and not suited for large amounts of data-sets, for example when data-sets from a large number of people have to be evaluated statistically.
Another approach has been published by Xiao Han, Chenyang Xu, Duygu Tosun, and Jerry L. Prince, “Cortical Surface Reconstruction Using a Topology Preserving Deformable Model,” IEEE Workshop on mathematical models in biomedical image analysis, Kauai Hi. 2001. This method is an automatic method to reconstruct the GM/WM, central and pial surfaces of the cerebral cortex from MR images. This method models sulci by removing voxels along their medial axes in the GM membership volume, and has therefore not the ability to model tight sulci with a subvoxel precision. The openings of the sulci are stopped at 1 mm distance from the fundus. The drawbacks are therefore that the distance between the sulcal banks are minimum 1 voxel even though the sulus is completely closed, and the cortical thickness at the fundus of tight sulcal folds are always 1 mm, which is presumed to be a lower bound of the cortical thickness, hence this method is also biased to a predefined distance.
U.S. Pat. No. 6,591,004 by VanEssen assigned to Washington University discloses a method called SUREFIT for reconstructing surfaces. This method is not fully automatic as the topology correction requires manual intervention. This makes the method tedious for large numbers of data-sets, for example when data-sets from a large number of subjects have to be evaluated statistically. Furthermore, this method has the disadvantage of not preventing self-intersections of the calculated surfaces, which especially makes modelling of sulci unreliable.
In the dissertation “Deformable models with application to human cerebreal cortex reconstruction from magnetic resonance images” by Chengyang Xu, published at Johns Hopkins University, Baltimore, Md., retrievable from Internet httl://iacl.ecejhu.edu/pubs/chenyang_xu_thesis.pdf, a model is disclosed for reconstruction of sulci. Fort this, a linear combination of a normal vector field with a gradient vector field is employed. The normal vector field is set identical to zero in the grey matter of the brain, as discussed on page 77 in this reference, such that the gradient vector field is the only external force.
Even though a number of methods are known according to the overview above, the methods still lack a reliable method for modeling the sulci, especially the bottom of the sulci, on the outer boundary of the cortex. However, especially the modeling of the sulci is important, if accurate measurements of the cortical thickness are to be achieved.